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A330082
a(n) = 5*A064038(n+1).
1
0, 5, 15, 15, 25, 75, 105, 70, 90, 225, 275, 165, 195, 455, 525, 300, 340, 765, 855, 475, 525, 1155, 1265, 690, 750, 1625, 1755, 945, 1015, 2175, 2325, 1240, 1320, 2805, 2975, 1575, 1665, 3515, 3705, 1950, 2050, 4305, 4515, 2365, 2475, 5175, 5405, 2820, 2940
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.
Compare to A319127 = 6 * A002620 in the hexagonal 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
FORMULA
a(n) = A026741(A028895(n)).
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
A330082[n_]:=5Numerator[n(n+1)/4]; Array[A330082, 100, 0] (* Paolo Xausa, Dec 04 2023 *)
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
Sequence in context: A291794 A321775 A166621 * A160275 A200858 A184288
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