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A227356 Partial sums of A129361. 1
1, 2, 5, 10, 20, 36, 65, 112, 193, 324, 544, 900, 1489, 2442, 4005, 6534, 10660, 17336, 28193, 45760, 74273, 120408, 195200, 316216, 512257, 829458, 1343077, 2174130, 3519412, 5696124, 9219105, 14919408, 24144289 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sum of labeled numbers of boxes arranged as Pyramid type-II with base Fibonacci(n).

Let us call a Pyramid "type-I" when each row starts with the same number as the leftmost base number, and "type-II" when each column has the same number as the base.

The Pyramid arrangements are related to other sequences as follows:

   Base Number     Type-I     Type-II

   -----------     ------     -------

   Natural         A002623    A034828

   Odd             A000292    A128624

   Fibonacci       A129696    a(n)

   1               A002620    A002620

   1,0             A008805

See illustration in links.

LINKS

Table of n, a(n) for n=1..33.

Kival Ngaokrajang, Illustration for some small n.

Index entries for linear recurrences with constant coefficients, signature (2,1,-3,1,-1,0,1).

FORMULA

For n >=2, a(n) = a(n-1) + A129361(n-1).

G.f. -x*(1+x)*(x^2-x+1) / ( (x-1)*(x^2+x-1)*(x^4+x^2-1) ). - Joerg Arndt, Jul 10 2013

a(n) = 2 + A000045(n+4) - A096748(n+6). - R. J. Mathar, Jul 20 2013

PROG

(Small Basic)

a[1] = 1

k = 0

s5 = Math.SquareRoot(5)

For n = 2 To 51

  If Math.Remainder(n, 2)=0 Then

    i = (n+2)/2

  Else

    i = (n+1)/2

  EndIf

  For j = i To n

    k = k + Math.Round(Math.Power((1+s5)/2, j)/s5)

  EndFor

  a[n] = a[n-1] + k

  TextWindow.Write(a[n-1] + ", ")

  k = 0

EndFor

CROSSREFS

Cf. A002623, A034828, A002620, A000292, A128624, A129696, A008805.

Sequence in context: A121597 A000712 A032442 * A102688 A236559 A275388

Adjacent sequences:  A227353 A227354 A227355 * A227357 A227358 A227359

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Jul 08 2013

STATUS

approved

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Last modified February 20 06:26 EST 2019. Contains 320332 sequences. (Running on oeis4.)