OFFSET
0,2
COMMENTS
Main column of a pentagonal spiral for A026741:
(25)
49 (15) 31
24 29 (15) 8 16
47 14 7 ( 5) 3 17 33
23 27 13 2 ( 0) 1 7 9 17
45 13 6 3 1 4 19 35
22 25 11 5 9 10 18
43 12 23 11 21 37
21 41 20 39 19
a(n) = 5 * A064038(n+1) from a pentagonal spiral.
22 23 23 22 (24)
20 12 13 13 (12) 25
21 10 5 4 ( 6) 14 25
21 11 5 1 ( 0) 7 15 24
20 11 4 1 ( 0) 2 7 15 26
18 10 2 3 3 6 14 27
19 8 9 9 8 16 27
19 18 16 17 17 26
30 28 29 29 28
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).
FORMULA
From Colin Barker, Dec 08 2019: (Start)
G.f.: 5*x*(1 + 4*x^3 + x^6) / ((1 - x)^3*(1 + x^2)^3).
a(n) = 3*a(n-1) - 6*a(n-2) + 10*a(n-3) - 12*a(n-4) + 12*a(n-5) - 10*a(n-6) + 6*a(n-7) - 3*a(n-8) + a(n-9) for n>8.
a(n) = (-5/16 + (5*i)/16)*(((-3-3*i) + (-i)^n + i^(1+n))*n*(1+n)) where i=sqrt(-1).
(End)
MATHEMATICA
PROG
(PARI) concat(0, Vec(5*x*(1 + 4*x^3 + x^6) / ((1 - x)^3*(1 + x^2)^3) + O(x^50))) \\ Colin Barker, Dec 08 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Dec 01 2019
EXTENSIONS
More terms from Colin Barker, Dec 22 2019
Name corrected by Paolo Xausa, Dec 04 2023
STATUS
approved