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A373961
Number of compositions of 6*n-1 into parts 5 and 6.
3
1, 2, 3, 4, 5, 7, 15, 44, 129, 340, 804, 1742, 3550, 7009, 13835, 28033, 58993, 128136, 282569, 622575, 1357136, 2918449, 6204578, 13104675, 27646776, 58502733, 124411595, 265807567, 569552644, 1221316021, 2616456236, 5595314908, 11944318042, 25466629978
OFFSET
1,2
FORMULA
a(n) = A017837(6*n-1).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-1-5*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*(1-x)^4/((1-x)^6 - x^5).
a(n) = A373962(n+1) - A373962(n).
PROG
(PARI) a(n) = sum(k=0, n\5, binomial(n+k, n-1-5*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 23 2024
STATUS
approved