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A243201 Odd octagonal numbers indexed by triangular numbers. 5
1, 21, 133, 481, 1281, 2821, 5461, 9633, 15841, 24661, 36741, 52801, 73633, 100101, 133141, 173761, 223041, 282133, 352261, 434721, 530881, 642181, 770133, 916321, 1082401, 1270101, 1481221, 1717633, 1981281, 2274181, 2598421, 2956161, 3349633, 3781141, 4253061, 4767841, 5328001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Column 5 of A081297.

Column 6 of A072024.

Diagonal T(n + 1, n) of A219069, n > 0.

LINKS

Table of n, a(n) for n=0..36.

FORMULA

a(n) = 3*n^4 + 6*n^3 + 7*n^2 + 4*n + 1.

a(n) = (n^2 + n + 1)*(3*n^2 + 3*n + 1).

a(n) = ((3*n^2 + 3*n + 2)^2 - 1)/3.

a(n) = A003215(n) * A002061(n + 1).

a(n) = A022522(n) / A005408(n).

a(n) = A081297(n, 5).

a(n) = A072024(n, 6).

a(n) = A219069(n + 1, n), n > 0.

a(n) = A000567(n^2 + n + 1).

a(n) = A014641((n^2 + n)/2).

a(n) = 1 + A140676(n^2 + n).

a(n) = 1 + A187156((n^2 + n + 4)/2) (empirical).

G.f.: (1 + 16*x + 38*x^2 + 16*x^3 + x^4)/(1 - x)^5. [Bruno Berselli, Jun 03 2014]

EXAMPLE

a(2) = 133 because the second triangular number is 3 and third odd octagonal number is 133.

a(3) = 481 because the third triangular number is 6 and the sixth odd octagonal number is 481.

a(4) = 1281 because the fourth triangular number is 10 and the tenth odd octagonal number is 1281.

MATHEMATICA

Table[((3 n^2 + 3 n + 2)^2 - 1)/3, {n, 0, 39}] (* Alonso del Arte, Jun 01 2014 *)

PROG

(MAGMA) [3*n^4+6*n^3+7*n^2+4*n+1: n in [0..40]]; // Bruno Berselli, Jun 03 2014

(Sage) [3*n^4+6*n^3+7*n^2+4*n+1 for n in (0..40)] # Bruno Berselli, Jun 03 2014

CROSSREFS

Cf. Row 5 of A059259 (coefficients of 1 + 4*n + 7*n^2 + 6*n^3 + 3*n^4 + 0*n^5 which is a formula for the within sequence).

Sequence in context: A008384 A110400 A089369 * A264554 A125331 A126489

Adjacent sequences:  A243198 A243199 A243200 * A243202 A243203 A243204

KEYWORD

nonn,easy

AUTHOR

Mathew Englander, Jun 01 2014

STATUS

approved

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Last modified September 20 16:14 EDT 2017. Contains 292276 sequences.