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A200048 Number of real singularities on a family of degree-3n algebraic surfaces. 2
4, 59, 220, 581, 1162, 2105, 3370, 5171, 7384, 10319, 13744, 18089, 22990, 29021, 35662, 43655, 52300, 62531, 73444, 86189, 99634, 115169, 131410, 150011, 169312, 191255, 213880, 239441, 265654, 295109, 325174, 358799, 392980, 431051, 469612, 512405, 555610 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence gives the number of real nodes of a family of algebraic surfaces with degrees 3n. They have been introduced by means of a kind of duality in the basic geometric constructions corresponding to the generation of substitution tilings.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

J. G. Escudero, A construction of algebraic surfaces with many real nodes, arXiv:1107.3401

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

FORMULA

a(n) = (1/12)*(135*n^3-126*n^2 + 45*n-6) if n is odd; a(n) = (1/12)*(135*n^3- 117*n^2 + 54*n - 12) if n is even.

From Colin Barker, Nov 04 2017: (Start)

G.f.: x*(4 + 55*x + 149*x^2 + 196*x^3 + 110*x^4 + 25*x^5 + x^6) / ((1 - x)^4*(1 + x)^3).

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.

(End)

PROG

(PARI) a(n) = if (n % 2, (1/12)*(135*n^3-126*n^2 + 45*n-6), (1/12)*(135*n^3- 117*n^2 + 54*n - 12)); \\ Michel Marcus, Aug 17 2013

(PARI) Vec(x*(4 + 55*x + 149*x^2 + 196*x^3 + 110*x^4 + 25*x^5 + x^6) / ((1 - x)^4*(1 + x)^3) + O(x^40)) \\ Colin Barker, Nov 04 2017

CROSSREFS

Sequence in context: A198511 A282040 A245827 * A037066 A113251 A183462

Adjacent sequences:  A200045 A200046 A200047 * A200049 A200050 A200051

KEYWORD

nonn,easy

AUTHOR

Juan G. Escudero, Nov 13 2011

EXTENSIONS

More terms from Michel Marcus, Aug 17 2013

STATUS

approved

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Last modified December 5 14:32 EST 2021. Contains 349557 sequences. (Running on oeis4.)