A238375 Row sums of triangle in A152719.
1, 2, 4, 6, 11, 16, 28, 40, 69, 98, 168, 238, 407, 576, 984, 1392, 2377, 3362, 5740, 8118, 13859, 19600, 33460, 47320, 80781, 114242, 195024, 275806, 470831, 665856, 1136688, 1607520, 2744209, 3880898, 6625108, 9369318, 15994427, 22619536, 38613964, 54608392
Offset: 0
Examples
Triangle A152719 and row sums: 1; ............................. sum = 1 1, 1; .......................... sum = 2 1, 2, 1; ....................... sum = 4 1, 2, 2, 1; ................... sum = 6 1, 2, 5, 2, 1; ............... sum = 11 1, 2, 5, 5, 2, 1; ............ sum = 16 1, 2, 5, 12, 5, 2, 1; ......... sum = 28 1, 2, 5, 12, 12, 5, 2, 1; ...... sum = 40
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,2,-2,1,-1).
Programs
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Mathematica
Table[Sum[Fibonacci[1+Min[k, n-k], 2], {k,0,n}], {n,0,45}] (* G. C. Greubel, May 21 2021 *) -
PARI
my(x='x+O('x^44)); Vec((1+x)/((1-2*x^2-x^4)*(1-x))) \\ Joerg Arndt, May 22 2021 -
Sage
def Pell(n): return n if (n<2) else 2*Pell(n-1) + Pell(n-2) def a(n): return sum(Pell(1+min(k, n-k)) for k in (0..n)) [a(n) for n in (0..45)] # G. C. Greubel, May 21 2021
Formula
a(n) = Sum_{k=0..n} A152719(n,k).
G.f.: (1+x)/((1-2*x^2-x^4)*(1-x)).
a(2*n) = A005409(n+2).
a(2*n+1) = 2*A048739(n).
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
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