A162460 First differences of A161762.

0, 2, 2, 7, 14, 37, 90, 232, 594, 1541, 4004, 10441, 27260, 71254, 186354, 487579, 1276002, 3339821, 8742470, 22885996, 59912930, 156848617, 410626152, 1075018897, 2814412824, 7368190922, 19290113570, 50502074767, 132215989334, 346145696821, 906220783314

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1).

Formula

a(n) = A161762(n+1) - A161762(n).

a(n) = A000217(A000045(n+1)) + A000217(A000045(n-1)-1) - A000290(A000045(n)). - R. J. Mathar, Jul 06 2009

From Colin Barker, Feb 25 2019: (Start)

G.f.: x^2*(2 - 4*x - x^2 + x^3) / ((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)).

a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - a(n-4) + a(n-5) for n>4.

(End)

Example

a(1) =  0 =  1 -  1.
a(2) =  2 =  3 -  1.
a(3) =  2 =  5 -  3.
a(4) =  7 = 12 -  5.
a(5) = 14 = 26 - 12.
a(6) = 37 = 63 - 26.

Maple

A000217 := proc(n) n*(n+1)/2 ; end:
A000045 := proc(n) combinat[fibonacci](n) ; end:
A162460 := proc(n) A161762(n+1)-A161762(n) ; end:
A161762 := proc(n) A000217(A000045(n))-A000217( A000045(n-1)-1) ; end: seq(A162460(n), n=1..80) ; # R. J. Mathar, Jul 06 2009

Prog

(PARI) concat(0, Vec(x^2*(2 - 4*x - x^2 + x^3) / ((1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)) + O(x^40))) \\ Colin Barker, Feb 25 2019

Crossrefs

Cf. A000045, A161762.

Sequence in context: A344048 A228432 A298959 * A187306 A061274 A061575

Adjacent sequences: A162457 A162458 A162459 * A162461 A162462 A162463

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jul 04 2009

Extensions

a(21) corrected by R. J. Mathar, Jul 05 2009

Status

approved