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 A056640 At stage 1, start with a unit square. At each successive stage add 4*(n-1) new squares around outside with edge-to-edge contacts. Sequence gives number of squares (regardless of size) at n-th stage. 5
 1, 5, 18, 42, 83, 143, 228, 340, 485, 665, 886, 1150, 1463, 1827, 2248, 2728, 3273, 3885, 4570, 5330, 6171, 7095, 8108, 9212, 10413, 11713, 13118, 14630, 16255, 17995, 19856, 21840, 23953, 26197, 28578, 31098, 33763, 36575, 39540, 42660, 45941, 49385, 52998 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of unit squares at n-th stage = n^2 + (n-1)^2 (A001844). First differences are in A255840. - Wesley Ivan Hurt, Mar 13 2015 REFERENCES Anthony Gardiner, "Mathematical Puzzling," Dover Publications, Inc., Mineola, NY., 1987, page 88. LINKS Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1). FORMULA G.f.: x(5x^2+2x+1)/((1-x^2)(1-x)^3). a(n) = (8*n^3-2*n+3-3*(-1)^n)/12. - Luce ETIENNE, Aug 21 2014 a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). - Colin Barker, Sep 29 2014 G.f.: x*(5*x^2+2*x+1) / ((x-1)^4*(x+1)). - Colin Barker, Sep 29 2014 MAPLE A056640:=n->(8*n^3-2*n+3-3*(-1)^n)/12: seq(A056640(n), n=1..50); MATHEMATICA Table[(8*n^3 - 2*n + 3 - 3*(-1)^n)/12, {n, 30}] (* Wesley Ivan Hurt, Mar 13 2015 *) PROG (PARI) Vec(x*(5*x^2+2*x+1)/((x-1)^4*(x+1)) + O(x^100)) \\ Colin Barker, Sep 29 2014 CROSSREFS Cf. A255840. Sequence in context: A352368 A000338 A212343 * A272703 A272736 A273532 Adjacent sequences: A056637 A056638 A056639 * A056641 A056642 A056643 KEYWORD nonn,easy AUTHOR Robert G. Wilson v, Aug 21 2000 EXTENSIONS More terms from Colin Barker, Sep 29 2014 STATUS approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)