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A373964
Number of compositions of 6*n-4 into parts 5 and 6.
3
0, 0, 0, 1, 5, 15, 35, 70, 127, 221, 396, 781, 1716, 4005, 9390, 21421, 47107, 100283, 208982, 432197, 898064, 1889152, 4028036, 8671852, 18739049, 40434205, 86861995, 185669195, 395358538, 840341619, 1786426005, 3803164340, 8111872645, 17329007156
OFFSET
1,5
FORMULA
a(n) = A017837(6*n-4).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-4-5*k).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).
G.f.: x^4*(1-x)/((1-x)^6 - x^5).
a(n) = A369794(n+1) - A369794(n).
PROG
(PARI) a(n) = sum(k=0, n\5, binomial(n+k, n-4-5*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 24 2024
STATUS
approved