A052255 Partial sums of A050484.

1, 13, 81, 345, 1155, 3267, 8151, 18447, 38610, 75790, 140998, 250614, 428298, 707370, 1133730, 1769394, 2696727, 4023459, 5888575, 8469175, 11988405, 16724565, 23021505, 31300425, 42073200, 55957356, 73692828, 96160636, 124403620, 159649380, 203335572, 257137716

Offset

0,2

References

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

Murray R.Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.

Links

Andrew Howroyd, 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) = (5*n+8)*binomial(n+7, 7)/8.

G.f.: (1+4*x)/(1-x)^9.

Sum_{n>=0} 1/a(n) = 1822946/15147 + (312500/5049)*(Pi/(5^(1/4)*phi^(3/2)) + sqrt(5)*log(phi) - 5*log(5)/2), where phi is the golden ratio (A001622). - Amiram Eldar, Nov 17 2025

Mathematica

a[n_] := (5*n+8) * Binomial[n+7, 7] / 8; Array[a, 30, 0] (* Amiram Eldar, Nov 17 2025 *)

Crossrefs

Cf. A001622, A050484.

Cf. A093562 ((5, 1) Pascal, column m=8).

Sequence in context: A189451 A133718 A241696 * A362545 A082203 A367118

Adjacent sequences: A052252 A052253 A052254 * A052256 A052257 A052258

Keyword

easy,nonn

Author

Barry E. Williams, Feb 02 2000

Extensions

a(24) onward from Andrew Howroyd, Nov 10 2025

Status

approved