A053367 Partial sums of A050494.

1, 11, 63, 255, 825, 2277, 5577, 12441, 25740, 50050, 92378, 163098, 277134, 455430, 726750, 1129854, 1716099, 2552517, 3725425, 5344625, 7548255, 10508355, 14437215, 19594575, 26295750, 34920756, 45924516, 59848228, 77331980, 99128700, 126119532, 159330732, 199952181, 249357615

Offset

0,2

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

a(n) = binomial(n+7, 7)*(3n+8)/8.

G.f.: (1+2*x)/(1-x)^9.

Mathematica

LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 11, 63, 255, 825, 2277, 5577, 12441, 25740}, 30] (* or *) Table[(3*n+8)* Binomial[n+7, 7]/8, {n, 0, 30}] (* G. C. Greubel, May 25 2018 *)

Prog

(PARI) a(n)=binomial(n+7, 7)*(3*n+8)/8 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [(3*n+8)*Binomial(n+7, 7)/8: n in [0..30]]; // G. C. Greubel, May 25 2018

Crossrefs

Cf. A050494.

Cf. A093560 ((3, 1) Pascal, column m=8).

Sequence in context: A301610 A298046 A120723 * A163706 A180763 A362164

Adjacent sequences: A053364 A053365 A053366 * A053368 A053369 A053370

Keyword

easy,nonn

Author

Barry E. Williams, Jan 06 2000

Extensions

Terms a(24) onward added by G. C. Greubel, May 25 2018

Status

approved