A246697 - OEIS

%I #24 May 14 2021 02:58:33

%S 1,5,16,34,67,111,178,260,373,505,676,870,1111,1379,1702,2056,2473,

%T 2925,3448,4010,4651,5335,6106,6924,7837,8801,9868,10990,12223,13515,

%U 14926,16400,18001,19669,21472,23346,25363,27455,29698,32020,34501,37065,39796

%N Row sums of the triangular array A246696.

%F 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.

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

%F Conjecture: a(n) = (2*n^3+6*n^2+9*n+4+n*(-1)^n)/4. - _Luce ETIENNE_, Oct 16 2016

%F 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

%e First 5 rows of A246694 preceded by sums

%e sum = 1: ...... 1;

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

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

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

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

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

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

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

%Y Cf. A246694, A246695, A246696.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Sep 02 2014

%E Corrected and edited by _M. F. Hasler_, Nov 17 2014