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A224813 Number of subsets of {1,2,...,n-12} without differences equal to 2, 4, 6, 8, 10 or 12. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 80, 100, 130, 169, 221, 289, 374, 484, 616, 784, 980, 1225, 1505, 1849, 2279, 2809, 3498, 4356, 5478, 6889, 8715, 11025, 13965, 17689, 22344, 28224, 35448, 44521, 55704, 69696, 87120, 108900, 136290, 170569, 213934, 268324, 337218, 423801, 533169, 670761, 843570 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,14

COMMENTS

a(n) is the number of permutations (p(1), p(2), ..., p(n)) satisfying -k <= p(i)-i <= r and p(i)-i in the set I, i=1..n, with k=2, r=12, I={-2,0,12}.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-13

FORMULA

a(n) = a(n-1) +a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11) -a(n-12) +a(n-13) +3*a(n-14) -2*a(n-15) +2*a(n-16) -a(n-17) +a(n-18) -3*a(n-21) +2*a(n-22) -4*a(n-23) +2*a(n-24) -3*a(n-25) -3*a(n-28) +a(n-29) -2*a(n-30) +3*a(n-35) -a(n-36) +3*a(n-37) +a(n-42) -a(n-49).

G.f.: -(-1 +x^7 +x^9 +x^11 +2*x^14 +x^16 -2*x^21 -2*x^23 -x^28 +x^35)/( (x^7+x-1) *(x^42 -x^36 -2*x^30 -3*x^28 +2*x^24 +2*x^22 +x^18 +2*x^16 +3*x^14 -x^12 -x^10 -x^8 -1) ).

a(2*k) = (A005709(k))^2, a(2*k+1) = A005709(k) * A005709(k+1).

MATHEMATICA

CoefficientList[Series[-(-1 + x^7 + x^9 + x^11 + 2*x^14 + x^16 - 2*x^21 - 2*x^23 - x^28 + x^35)/((x^7 + x - 1)*(x^42 - x^36 - 2*x^30 - 3*x^28 + 2*x^24 + 2*x^22 + x^18 + 2*x^16 + 3*x^14 - x^12 - x^10 - x^8 - 1)), {x, 0, 1000}], x] (* G. C. Greubel, Oct 28 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(-(-1 + x^7 + x^9 + x^11 + 2*x^14 + x^16 - 2*x^21 - 2*x^23 - x^28 + x^35)/((x^7 + x - 1)*(x^42 - x^36 - 2*x^30 - 3*x^28 + 2*x^24 + 2*x^22 + x^18 + 2*x^16 + 3*x^14 - x^12 - x^10 - x^8 - 1))) \\ G. C. Greubel, Oct 28 2017

CROSSREFS

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A217694, A224808-A224815.

Sequence in context: A002620 A087811 A025699 * A224812 A194256 A194246

Adjacent sequences:  A224810 A224811 A224812 * A224814 A224815 A224816

KEYWORD

nonn,easy

AUTHOR

Vladimir Baltic, May 18 2013

STATUS

approved

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Last modified October 23 16:15 EDT 2018. Contains 316529 sequences. (Running on oeis4.)