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

Offset: 0

Author

Paul Curtz, Dec 01 2019

Keywords

• nonn
• easy

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

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).

Crossrefs

Cf. A026741, A028895, A064038. A033429, A062786, A087348, A147874, A158447, A168668 are in the spiral.

Programs

Mathematica

A330082[n_]:=5Numerator[n(n+1)/4];Array[A330082,100,0] (* Paolo Xausa, Dec 04 2023 *)

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

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)

Extensions

More terms from Colin Barker, Dec 22 2019

Name corrected by Paolo Xausa, Dec 04 2023