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A246695 Row sums of the triangular array A246694.

%I A246695 #32 Nov 23 2024 10:06:30
%S A246695 1,3,9,18,35,57,91,132,189,255,341,438,559,693,855,1032,1241,1467,
%T A246695 1729,2010,2331,2673,3059,3468,3925,4407,4941,5502,6119,6765,7471,
%U A246695 8208,9009,9843,10745,11682,12691,13737,14859,16020,17261,18543,19909,21318,22815
%N A246695 Row sums of the triangular array A246694.
%C A246695 Also partial sums of A257083. - _Reinhard Zumkeller_, Apr 17 2015
%H A246695 Reinhard Zumkeller, <a href="/A246695/b246695.txt">Table of n, a(n) for n = 0..10000</a>
%F A246695 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.
%F A246695 Conjectured g.f.: (1 + x + 2*x^2 + x^3 + x^4)/((x - 1)^4*(x + 1)^2).
%F A246695 Conjecture: a(n) = (1/8)*(n + 1)*((-1)^n + 2*n^2 + 4*n + 7). - _Eric Simon Jacob_, Jul 19 2023 [This conjecture is correct; compare A377802, note offset 1. - _Werner Schulte_, Nov 22 2024]
%e A246695 First 5 rows of A246694 preceded by sums
%e A246695 sum = 1: ...... 1
%e A246695 sum = 3: ...... 1 ... 2
%e A246695 sum = 9: ...... 3 ... 2 ... 4
%e A246695 sum = 18: ..... 3 ... 5 ... 4 ... 6
%e A246695 sum = 35: ..... 7 ... 5 ... 8 ... 6 ... 9
%t A246695 z = 25; t[0, 0] = 1; t[1, 0] = 1; t[1, 1] = 2;
%t A246695 t[n_, 0] := If[OddQ[n], t[n - 1, n - 2] + 1, t[n - 1, n - 1] + 1];
%t A246695 t[n_, 1] := If[OddQ[n], t[n - 1, n - 1] + 1, t[n - 1, n - 2] + 1];
%t A246695 t[n_, k_] := t[n, k - 2] + 1; A246695 = Table[Sum[t[n, k], {k, 0, n}], {n, 0, z}]
%o A246695 (Haskell)
%o A246695 a246695 n = a246695_list !! n
%o A246695 a246695_list = scanl1 (+) a257083_list
%o A246695 -- _Reinhard Zumkeller_, Apr 17 2015
%Y A246695 Cf. A246694, A246705, A246706.
%Y A246695 Cf. A257083, A377802.
%K A246695 nonn,easy
%O A246695 0,2
%A A246695 _Clark Kimberling_, Sep 01 2014
%E A246695 Corrected and edited by _M. F. Hasler_, Nov 17 2014