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A263134
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a(n) = Sum_{k=0..n} binomial(3*k+1,k).
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4
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1, 5, 26, 146, 861, 5229, 32361, 202905, 1284480, 8191380, 52543545, 338641305, 2191124301, 14224347181, 92603307541, 604342068085, 3952451061076, 25898039418496, 169977746765071, 1117287239602471, 7353933943361866, 48461930821297546
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OFFSET
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0,2
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COMMENTS
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Primes in sequence: 5, 92603307541, 52176309488123582020412161, ...
a(n) is divisible by n for n = 1, 2, 8, 55, 82, 171, 210, 1060, 1141, ...
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LINKS
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FORMULA
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Recurrence: 2*n*(2*n + 1)*a(n) = (31*n^2 + 2*n - 3)*a(n-1) - 3*(3*n - 1)*(3*n + 1)*a(n-2). - Vaclav Kotesovec, Oct 11 2015
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MATHEMATICA
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Table[Sum[Binomial[3 k + 1, k], {k, 0, n}], {n, 0, 25}]
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PROG
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(Sage) [sum(binomial(3*k+1, k) for k in (0..n)) for n in (0..25)]
(Magma) [&+[Binomial(3*k+1, k): k in [0..n]]: n in [0..25]];
(Maxima) makelist(sum(binomial(3*k+1, k), k, 0, n), n, 0, 25);
(PARI) a(n) = sum(k=0, n, binomial(3*k+1, k)) \\ Colin Barker, Oct 16 2015
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CROSSREFS
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Cf. A079309: Sum_{k=0..n} binomial(2*k+1,k).
Cf. A188675: Sum_{k=0..n} binomial(3*k,k).
Cf. A087413: Sum_{k=0..n} binomial(3*k+2,k).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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