A107601 Column 6 of array illustrated in A089574 and related to A034261.

7, 71, 350, 1204, 3329, 7936, 16981, 33452, 61719, 107953, 180620, 291056, 454129, 688994, 1019947, 1477384, 2098871, 2930331, 4027354, 5456636, 7297553, 9643876, 12605633, 16311124, 20909095, 26571077, 33493896, 41902360, 52052129

Offset

0,1

Comments

Column six is associated with the following partitions: 66, 552, 443, 4422, 3332, 33222 and 222222.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = A107601(10+n,5+n) = n*(1384+4683*n^2+2142*n+2*n^6+651*n^4+63*n^5+2835*n^3)/1680. a(n)= +8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). G.f.: x*(7+15*x-22*x^2+11*x^4-6*x^5+x^6)/(x-1)^8. - R. J. Mathar, Jun 26 2010

Example

a(1) = 7 because there are 3 permutations of 443 and 4 permutations of 3332.
a(2) = 71 because there are 1 + 3 + 18 + 6 + 32 + 10 + 1 permutations of the associated partitions.

Prog

(PARI) a(n)=(2*n^7+77*n^6+1071*n^5+7105*n^4+23863*n^3+40698*n^2+34704*n+11760)/1680 \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A107600.

Sequence in context: A069619 A137443 A362106 * A175863 A196742 A196900

Adjacent sequences: A107598 A107599 A107600 * A107602 A107603 A107604

Keyword

nonn,easy

Author

Alford Arnold, May 27 2005

Extensions

Extended beyond a(5) by R. J. Mathar, Jun 26 2010

Status

approved