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A238375 Row sums of triangle in A152719. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

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

CROSSREFS

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

Sequence in context: A103692 A114921 A103442 * A056342 A094719 A294811

Adjacent sequences:  A238372 A238373 A238374 * A238376 A238377 A238378

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Feb 25 2014

STATUS

approved

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Last modified June 24 08:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)