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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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) from a pentagonal spiral.
Compare to A319127(n) = 6 * A002620(n) 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
A319127(n) = 0, 0, 6, 12, 24, 36, 54, 72, 96, ... .
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LINKS
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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).
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FORMULA
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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)
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PROG
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(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
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CROSSREFS
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Cf. A026741, A028895, A064038. A033429, A062786, A087348, A147874, A158447, A168668 are in the spiral.
Sequence in context: A291794 A321775 A166621 * A160275 A200858 A184288
Adjacent sequences: A330079 A330080 A330081 * A330083 A330084 A330085
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Dec 01 2019
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EXTENSIONS
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More terms from Colin Barker, Dec 22 2019
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STATUS
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approved
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