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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
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 (list; graph; refs; listen; history; text; internal format)
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 * A299256 A002411 A023658

Adjacent sequences:  A122058 A122059 A122060 * A122062 A122063 A122064

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)