A277975 a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=5.

1, 6, 56, 431, 2931, 18556, 112306, 659181, 3784181, 21362306, 119018556, 656127931, 3585815431, 19454956056, 104904174806, 562667846681, 3004074096681, 15974044799806, 84638595581056, 447034835815431, 2354383468627931, 12367963790893556, 64820051193237306

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-35,25).

Formula

G.f.: (1 - 5*x + 25*x^2)/((1 - x)*(1 - 5*x)^2).

a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3) for n>2.

a(n) = (21 - 5^(1+n) + 4*5^(1+n)*n)/16.

Example

a(3) = 3*5^3 + (3-1)*5^(3-1) + 5 + 1 = 431.

Mathematica

LinearRecurrence[{11, -35, 25}, {1, 6, 56}, 30] (* Harvey P. Dale, Jul 15 2020 *)

Prog

(PARI) Vec((1-5*x+25*x^2)/((1-x)*(1-5*x)^2) + O(x^30)) \\ Colin Barker, Nov 07 2016

Crossrefs

Cf. A088581, A088582.

Sequence in context: A074018 A074016 A183513 * A347718 A155613 A183586

Adjacent sequences: A277972 A277973 A277974 * A277976 A277977 A277978

Keyword

nonn,easy

Author

Colin Barker, Nov 07 2016

Status

approved