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

Author

Amarnath Murthy, Aug 24 2005

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A111710, A111712, A080512, A257143.

Programs

Haskell

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

Mathematica

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

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

Extensions

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