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A246697 Row sums of the triangular array A246696. 5
1, 5, 16, 34, 67, 111, 178, 260, 373, 505, 676, 870, 1111, 1379, 1702, 2056, 2473, 2925, 3448, 4010, 4651, 5335, 6106, 6924, 7837, 8801, 9868, 10990, 12223, 13515, 14926, 16400, 18001, 19669, 21472, 23346, 25363, 27455, 29698, 32020, 34501, 37065, 39796 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..42.

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) = 5, a(2) = 16, a(3) = 34, a(4) = 67, a(5) = 111, a(6) = 178.

Conjectured g.f.: (1 + 3*x + 5*x^2 + x^3 + 2*x^4)/((x - 1)^4*(x + 1)^2).

Conjecture: a(n) = (2*n^3+6*n^2+9*n+4+n*(-1)^n)/4. - Luce ETIENNE, Oct 16 2016

Conjectured e.g.f.: ((2 + 8*x + 6*x^2 + x^3)*cosh(x) + (2 + 9*x + 6*x^2 + x^3)*sinh(x))/2. - Stefano Spezia, May 10 2021

EXAMPLE

First 5 rows of A246694 preceded by sums

sum = 1: ...... 1;

sum = 5: ...... 2 ... 3;

sum = 16: ..... 5 ... 4 ... 7;

sum = 34: ..... 6 ... 9 ... 8 ... 11;

sum = 67: ..... 13 .. 10 .. 15 .. 12 .. 17.

MATHEMATICA

z = 25; t[0, 0] = 1; t[1, 0] = 2; t[1, 1] = 3; t[n_, 0] := t[n, 0] = If[OddQ[n], t[n - 1, n - 2] + 2, t[n - 1, n - 1] + 2]; t[n_, 1] := t[n, 1] = If[OddQ[n], t[n - 1, n - 1] + 2, t[n - 1, n - 2] + 2]

t[n_, k_] := t[n, k] = t[n, k - 2] + 2;

u = Flatten[Table[t[n, k], {n, 0, z}, {k, 0, n}]] (* A246696 *)

Table[Sum[t[n, k], {k, 0, n}], {n, 0, 2*z}] (* A246697 *)

CROSSREFS

Cf. A246694, A246695, A246696.

Sequence in context: A131425 A227720 A096941 * A098404 A190970 A077415

Adjacent sequences:  A246694 A246695 A246696 * A246698 A246699 A246700

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 02 2014

EXTENSIONS

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

STATUS

approved

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Last modified July 25 21:44 EDT 2021. Contains 346294 sequences. (Running on oeis4.)