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A099253
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(7*n+6)-th terms of expansion of 1/(1-x-x^7).
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7
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1, 8, 43, 211, 1030, 5055, 24851, 122166, 600470, 2951330, 14505951, 71297834, 350434385, 1722411860, 8465785506, 41609980404, 204516223418, 1005212819668, 4940697593195, 24283905085013, 119357243593561, 586649945651116
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/((1-x)^7 - x);
a(n) = 8*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7).
a(n) = Sum_{k=0..n} binomial(7*n - 6*(k-1), k).
a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), k + 6*(k+1)).
a(n) = Sum_{k=0..n} binomial(n + 6*(k+1), n-k).
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MATHEMATICA
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Table[Sum[Binomial[7*n-6*(j-1), j], {j, 0, n}], {n, 0, 30}] (* G. C. Greubel, Mar 09 2021 *)
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PROG
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(Sage) [sum(binomial(7*n-6*j+6, j) for j in (0..n)) for n in (0..30)] # G. C. Greubel, Mar 09 2021
(Magma) [(&+[Binomial(7*n-6*j+6, j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 09 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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