A122061 First pentagonal number, 2nd hexagonal number, 3rd heptagonal number, 4th octagonal number and then repeat the same pattern: 5th pentagonal, 6th hexagonal, 7th heptagonal, 8th octagonal, etc.

1, 6, 18, 40, 35, 66, 112, 176, 117, 190, 286, 408, 247, 378, 540, 736, 425, 630, 874, 1160, 651, 946, 1288, 1680, 925, 1326, 1782, 2296, 1247, 1770, 2356, 3008, 1617, 2278, 3010, 3816, 2035, 2850, 3744, 4720, 2501, 3486, 4558, 5720, 3015, 4186, 5452

Offset

1,2

Comments

From a quiz.

References

A. Wareham, Test Your Brain Power, Ward Lock Ltd (1995).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1).

Formula

a(n) = n*(3*n-1)/2 if n=1 mod 4 or n*(4*n-2)/2 if n=2 mod 4 or n*(5*n-3)/2 if n=3 mod 4 or n*(6*n-4)/2 if n=0 mod 4

a(n)=3*a(n-4)-3*a(n-8)+a(n-12) for n>11. - Harvey P. Dale, Mar 01 2015

Mathematica

fn[n_]:=Module[{r=Mod[n, 4]}, Which[r==1, (n(3n-1))/2, r==2, (n(4n-2))/2, r==3, (n(5n-3))/2, r==0, (n(6n-4))/2]]; Array[fn, 50] (* or *) LinearRecurrence[ {0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 6, 18, 40, 35, 66, 112, 176, 117, 190, 286, 408}, 50] (* Harvey P. Dale, Mar 01 2015 *)

Prog

(PARI) for(n=1, 60, m=(n+3)%4; print1(n*((m+3)*n-m-1)/2, ", "))

Crossrefs

Cf. A060354.

Sequence in context: A271541 A035489 A219143 * A333713 A299256 A002411

Adjacent sequences: A122058 A122059 A122060 * A122062 A122063 A122064

Keyword

nonn

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 14 2006

Status

approved