A238375 - OEIS

%I #16 May 23 2021 02:53:04

%S 1,2,4,6,11,16,28,40,69,98,168,238,407,576,984,1392,2377,3362,5740,

%T 8118,13859,19600,33460,47320,80781,114242,195024,275806,470831,

%U 665856,1136688,1607520,2744209,3880898,6625108,9369318,15994427,22619536,38613964,54608392

%N Row sums of triangle in A152719.

%H G. C. Greubel, <a href="/A238375/b238375.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,1,-1).

%F a(n) = Sum_{k=0..n} A152719(n,k).

%F G.f.: (1+x)/((1-2*x^2-x^4)*(1-x)).

%F a(2*n) = A005409(n+2).

%F a(2*n+1) = 2*A048739(n).

%F a(n) = (-4 + 2*(1+(-1)^n)*Pell((n+4)/2) + (1-(-1)^n)*Q((n+3)/2))/4, where Pell(n) = A000129(n) and Q(n) = A002203(n). - _G. C. Greubel_, May 21 2021

%F a(n) = a(n-1)+2*a(n-2)-2*a(n-3)+a(n-4)-a(n-5). - _Wesley Ivan Hurt_, May 22 2021

%e Triangle A152719 and row sums:

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

%e   1, 1;  .......................... sum =  2

%e   1, 2, 1;  ....................... sum =  4

%e   1, 2, 2,  1;  ................... sum =  6

%e   1, 2, 5,  2,  1;  ............... sum = 11

%e   1, 2, 5,  5,  2, 1;  ............ sum = 16

%e   1, 2, 5, 12,  5, 2, 1;  ......... sum = 28

%e   1, 2, 5, 12, 12, 5, 2, 1;  ...... sum = 40

%t Table[Sum[Fibonacci[1+Min[k, n-k], 2], {k,0,n}], {n,0,45}] (* _G. C. Greubel_, May 21 2021 *)

%o (Sage)

%o def Pell(n): return n if (n<2) else 2*Pell(n-1) + Pell(n-2)

%o def a(n): return sum(Pell(1+min(k, n-k)) for k  in (0..n))

%o [a(n) for n in (0..45)] # _G. C. Greubel_, May 21 2021

%o (PARI) my(x='x+O('x^44)); Vec((1+x)/((1-2*x^2-x^4)*(1-x))) \\ _Joerg Arndt_, May 22 2021

%Y Cf. A000129, A002203, A005409, A048739, A135153 (first differences), A152719.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Feb 25 2014