[hzmsh]

When users pass a DateOffset such as DateOffset(months=1) to resample, or to Grouper(freq=...), they get NotImplementedError: Prefix not defined, even though the resample docs say rule can be a DateOffset.

import pandas as pd

df = pd.DataFrame(
    {
        "Timestamp": pd.date_range("2020-01-01", "2020-03-01", periods=5),
        "Amount": [5, 10, 15, 20, 25],
    }
)
df.resample(pd.DateOffset(months=1), on="Timestamp").sum()
df.groupby(pd.Grouper(key="Timestamp", freq=pd.DateOffset(months=1))).sum()
# main:    both raise NotImplementedError: Prefix not defined
# this PR: both return
#             Amount
# Timestamp
# 2020-01-01      30
# 2020-02-01      20
# 2020-03-01      25

Cause:

• Most pandas frequencies have a rule_code, a short name such as "ME" (month end) or "W" (weekly).
• resample and Grouper(freq=...) both do their time binning in the TimeGrouper class. It reads freq.rule_code in two places (__init__ and _adjust_bin_edges), only to check whether the frequency is anchored to the end of a period, like month end or week.
• DateOffset(months=1) adds one month but has no rule_code, so when TimeGrouper reads it, it raises Prefix not defined, and both resample and Grouper fail.

Fix:

• This PR adds a small helper, _rule_code(freq), that returns "" when the frequency has no rule_code, following the existing handling in DatetimeIndexOpsMixin._parse_with_reso.
• With "", both checks in TimeGrouper go to their else branch:
  1. __init__: closed and label default to "left", the same as for ordinary frequencies like "D".
  2. _adjust_bin_edges: the bin edges are used as they are, without the end-of-period adjustment.

Behavior change:

• Only calls that raised NotImplementedError: Prefix not defined before are affected.

• A generic DateOffset has no anchor, so the bins start at the date of the first timestamp, the same dates date_range gives. For example, data starting on 2024-01-15 gives bins on 01-15, 02-15, 03-15.

• Easter() had the same error and now works too.

• Not fixed here: a sub-daily DateOffset such as DateOffset(hours=12) on intraday data now raises ValueError: Values falls after last bin, the same root cause as BUG: resample by BusinessHour raises ValueError #12351 (being fixed for BusinessHour in BUG: resample with BusinessHour raises or mislabels bins (GH#12351) #71886).

• closes DataFrame.resample() breaks when rule parameter is of type DateOffset #31697

• Tests added and passed if fixing a bug or adding a new feature

• All code checks passed.

• Added type annotations to new arguments/methods/functions.

• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

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AI use: I worked with Claude Code (claude opus 5.5 (high)). Together we identified the root cause, wrote the fix and tests, and ran the new tests. It also helped turn my drafts and thoughts into this description. I also used gemini argon (high) for an additional review and audit.