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A330082 a(n) = 5*A064038(n). 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 (list; graph; refs; listen; history; text; internal format)
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) 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, ... .

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

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)

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

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

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 01 2019

EXTENSIONS

More terms from Colin Barker, Dec 22 2019

STATUS

approved

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Last modified September 19 13:31 EDT 2021. Contains 347563 sequences. (Running on oeis4.)