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A265056
Partial sums of A234275.
2
1, 5, 21, 45, 77, 117, 165, 221, 285, 357, 437, 525, 621, 725, 837, 957, 1085, 1221, 1365, 1517, 1677, 1845, 2021, 2205, 2397, 2597, 2805, 3021, 3245, 3477, 3717, 3965, 4221, 4485, 4757, 5037, 5325, 5621, 5925, 6237, 6557, 6885, 7221, 7565, 7917, 8277, 8645, 9021, 9405, 9797, 10197, 10605, 11021
OFFSET
0,2
COMMENTS
The number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 899", based on the 5-celled von Neumann neighborhood, initiated with a single black (ON) cell.- Robert Price, May 28 2016
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
FORMULA
From Colin Barker, Jan 01 2016: (Start)
a(n) = 4*n^2+4*n-3 for n>0.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.
G.f.: (1+2*x+9*x^2-4*x^3) / (1-x)^3.
(End)
MATHEMATICA
Accumulate[LinearRecurrence[{2, -1}, {1, 4, 16, 24}, 60]] (* or *) LinearRecurrence[{3, -3, 1}, {1, 5, 21, 45}, 60] (* Harvey P. Dale, Sep 22 2024 *)
PROG
(PARI) Vec((1+2*x+9*x^2-4*x^3)/(1-x)^3 + O(x^100)) \\ Colin Barker, Jan 01 2016
CROSSREFS
Cf. A234275.
Apart from initial term, same as A078371.
Sequence in context: A031292 A147331 A078371 * A049741 A166010 A146846
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 28 2015
STATUS
approved