A246695 Row sums of the triangular array A246694.

1, 3, 9, 18, 35, 57, 91, 132, 189, 255, 341, 438, 559, 693, 855, 1032, 1241, 1467, 1729, 2010, 2331, 2673, 3059, 3468, 3925, 4407, 4941, 5502, 6119, 6765, 7471, 8208, 9009, 9843, 10745, 11682, 12691, 13737, 14859, 16020, 17261, 18543, 19909, 21318, 22815

Offset

0,2

Comments

Also partial sums of A257083. - Reinhard Zumkeller, Apr 17 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

Conjectured linear recurrence: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6), with a(0) = 1, a(1) = 3, a(2) = 9, a(3) = 18, a(4) = 35, a(5) = 57, a(6) = 91.

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

Conjecture: a(n) = (1/8)*(n + 1)*((-1)^n + 2*n^2 + 4*n + 7). - Eric Simon Jacob, Jul 19 2023

Example

First 5 rows of A246694 preceded by sums
sum = 1: ...... 1
sum = 3: ...... 1 ... 2
sum = 9: ...... 3 ... 2 ... 4
sum = 18: ..... 3 ... 5 ... 4 ... 6
sum = 35: ..... 7 ... 5 ... 8 ... 6 ... 9

Mathematica

z = 25; t[0, 0] = 1; t[1, 0] = 1; t[1, 1] = 2;
t[n_, 0] := If[OddQ[n], t[n - 1, n - 2] + 1, t[n - 1, n - 1] + 1];
t[n_, 1] := If[OddQ[n], t[n - 1, n - 1] + 1, t[n - 1, n - 2] + 1];
t[n_, k_] := t[n, k - 2] + 1; A246695 = Table[Sum[t[n, k], {k, 0, n}], {n, 0, z}]

Prog

(Haskell)
a246695 n = a246695_list !! n
a246695_list = scanl1 (+) a257083_list
-- Reinhard Zumkeller, Apr 17 2015

Crossrefs

Cf. A246694, A246705, A246706.

Cf. A257083.

Sequence in context: A210970 A293406 A295862 * A132920 A127645 A000241

Adjacent sequences: A246692 A246693 A246694 * A246696 A246697 A246698

Keyword

nonn,easy

Author

Clark Kimberling, Sep 01 2014

Extensions

Corrected and edited by M. F. Hasler, Nov 17 2014

Status

approved