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A265676 a(n) is the total number of petals of the Flower of Life at the n-th iteration. 1
0, 1, 7, 19, 43, 67, 97, 139, 181, 229, 289, 349, 415, 493, 571, 655, 751, 847, 949, 1063, 1177, 1297, 1429, 1561, 1699, 1849, 1999, 2155, 2323, 2491, 2665, 2851, 3037, 3229, 3433, 3637, 3847, 4069, 4291, 4519, 4759, 4999, 5245, 5503, 5761, 6025, 6301, 6577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Inspired by A264788, but counting on petals of the Flower of Life instead of circles. For n >= 3, the second differences seem to be cyclic of 6, 12, 0.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Crystalinks, Flower of Life

Kival Ngaokrajang, Illustration of initial terms, For n = 11

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

FORMULA

From Colin Barker, Dec 13 2015: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>5.

G.f.: x*(1+5*x+6*x^2+11*x^3-5*x^4) / ((1-x)^3*(1+x+x^2)).

(End)

MATHEMATICA

CoefficientList[Series[x (1 + 5 x + 6 x^2 + 11 x^3 - 5 x^4)/((1 - x)^3 (1 + x + x^2)), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 14 2015 *)

PROG

(PARI) { a = 7; d1 = 6; print1("0, 1, ", a, ", "); for(n = 3, 100, if (Mod(n, 3) == 0, d2 = 6); if (Mod(n, 3) == 1, d2 = 12); if (Mod(n, 3) == 2, d2 = 0); d1 = d1 + d2; a = a + d1; print1(a, ", "))}

(PARI) concat(0, Vec(x*(1+5*x+6*x^2+11*x^3-5*x^4) / ((1-x)^3*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Dec 13 2015

(MAGMA) I:=[0, 1, 7, 19, 43, 67]; [n le 6 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-3)-2*Self(n-4)+Self(n-5): n in [1..60]]; // Vincenzo Librandi, Dec 14 2015

CROSSREFS

Cf. A264788.

Sequence in context: A141193 A104163 A145993 * A054690 A259486 A298034

Adjacent sequences:  A265673 A265674 A265675 * A265677 A265678 A265679

KEYWORD

nonn,easy

AUTHOR

Kival Ngaokrajang, Dec 13 2015

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)