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A094952 A sequence derived from pentagonal numbers, or a Stirling number of the first kind matrix. 2
6, 35, 105, 234, 440, 741, 1155, 1700, 2394, 3255, 4301, 5550, 7020, 8729, 10695, 12936, 15470, 18315, 21489, 25010, 28896, 33165, 37835, 42924, 48450, 54431, 60885, 67830, 75284, 83265, 91791, 100880, 110550, 120819, 131705, 143226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

R. Aldrovandi, "Special Matrices of Mathematical Physics", World Scientific, 2001, 13.3.1 "Inverting Bell Matrices", p. 171.

LINKS

Table of n, a(n) for n=1..36.

M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013

FORMULA

a(n) = (2n+1)*A005449(n) where A005449 = 2, 7, 15, 26, 40... Given the 4th order Stirling number of the first kind matrix [1 0 0 0 / -1 1 0 0 / 2 -3 1 0 / -6 11 -6 1] = M, M^n * [1 0 0 0] = [1 -n A005449(n) -a(n)]

Empirical G.f.: x*(6+11*x+x^2)/(1-x)^4. [Colin Barker, Jan 14 2012]

EXAMPLE

a(5) = 440 = (2n+1)*A005449(n) = 11 * 40.

a(6) = 741 since M^7 * [1 0 0 0] = [1 -6 57 -741].

MATHEMATICA

a[n_] := (MatrixPower[{{1, 0, 0, 0}, {-1, 1, 0, 0}, {2, -3, 1, 0}, {-6, 11, -6, 1}}, n].{{1}, {0}, {0}, {0}})[[4, 1]]; Table[ Abs[ a[n]], {n, 36}] (* Robert G. Wilson v, Jun 05 2004 *)

CROSSREFS

Cf. A005449.

Sequence in context: A009583 A033578 A101077 * A024526 A213504 A089581

Adjacent sequences:  A094949 A094950 A094951 * A094953 A094954 A094955

KEYWORD

nonn

AUTHOR

Gary W. Adamson, May 26 2004

EXTENSIONS

Edited by Robert G. Wilson v, Jun 05 2004

STATUS

approved

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)