A111711 Leading column of triangle mentioned in A111710.

1, 2, 5, 8, 14, 19, 28, 35, 47, 56, 71, 82, 100, 113, 134, 149, 173, 190, 217, 236, 266, 287, 320, 343, 379, 404, 443, 470, 512, 541, 586, 617, 665, 698, 749, 784, 838, 875, 932, 971, 1031, 1072, 1135, 1178, 1244, 1289, 1358, 1405, 1477, 1526, 1601, 1652

Offset

1,2

Comments

Also partial sums of A257143. - Reinhard Zumkeller, Apr 17 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

a(1)=1, a(2n) = a(2n-1)+2n-1, a(2n+1)=a(2n)+3n; a(n) = A111710(n-1)+1. - Franklin T. Adams-Watters, May 01 2006

From Chai Wah Wu, Mar 05 2021: (Start)

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

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

a(n) = (10*n*(n-1) + (-1)^n*(1-2*n)+15)/16. - Eric Simon Jacob, Jun 11 2022

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {1, 2, 5, 8, 14}, 60] (* Harvey P. Dale, Jun 21 2023 *)

Prog

(Haskell)
a111711 n = a111711_list !! (n-1)
a111711_list = 1 : zipWith (+) a111711_list a080512_list
-- Reinhard Zumkeller, Apr 17 2015

Crossrefs

Cf. A111710, A111712, A080512, A257143.

Sequence in context: A190105 A295400 A266287 * A095348 A215725 A022907

Adjacent sequences: A111708 A111709 A111710 * A111712 A111713 A111714

Keyword

easy,nonn

Author

Amarnath Murthy, Aug 24 2005

Extensions

More terms from Franklin T. Adams-Watters, May 01 2006

Status

approved