A050484 Partial sums of A051946.

1, 12, 68, 264, 810, 2112, 4884, 10296, 20163, 37180, 65208, 109616, 177684, 279072, 426360, 635664, 927333, 1326732, 1865116, 2580600, 3519230, 4736160, 6296940, 8278920, 10772775, 13884156, 17735472, 22467808, 28242984, 35245760

Offset

0,2

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = C(n+6, 6)*(5n+7)/7.

G.f.: (1+4*x)/(1-x)^8.

Mathematica

CoefficientList[Series[(1 + 4 x)/(1 - x)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 30 2014 *)
Accumulate[CoefficientList[Series[(1+4x)/(1-x)^7, {x, 0, 40}], x]] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 12, 68, 264, 810, 2112, 4884, 10296}, 30] (* Harvey P. Dale, Aug 21 2020 *)

Prog

(Magma) [((5*n+7)*Binomial(n+6, 6))/7: n in [0..60]]; // Vincenzo Librandi, Jul 30 2014
(PARI) a(n)=binomial(n+6, 6)*(5*n+7)/7 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A051946, A093562 ((5, 1) Pascal, column m=7).

Sequence in context: A200205 A059585 A213547 * A359715 A238536 A096425

Adjacent sequences: A050481 A050482 A050483 * A050485 A050486 A050487

Keyword

easy,nonn

Author

Barry E. Williams, Dec 26 1999

Status

approved