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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 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.)