0,3

Mean of first four nonnegative powers of 2n+1, i.e. ((2n+1)^0+(2n+1)^1+(2n+1)^2+(2n+1)^3)/4. E.g. a(2)=(1+3+9+27)/4=10

Equatorial structured meta-diamond numbers, the n-th number from an equatorial structured n-gonal diamond number sequence. There are no 1- or 2-gonal diamonds, so 1 and (n+2) are used as the first and second terms since all the sequences begin as such. - James A. Record (james.record(AT)gmail.com). Nov 07, 2004

Starting with offset 1 = row sums of triangle A143803. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Harry J. Smith, Table of n, a(n) for n=0,...,1000

a(n) = A053698(2n+1)/4

a(n) = sum (((n+j-1)^2-j^2+1),j=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 13 2006

G.f.: x(1+x)(1+5x)/(1-x)^4. a(n)= A002414(n-1)+A002414(n). a(n+1)-a(n)=A136392(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]

(PARI) { for (n=0, 1000, write("b059722.txt", n, " ", n*(2*n^2 - 2*n + 1)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 28 2009]

Cf. A000330, A005900, A081436, A100178, A100179, A059722: "equatorial" structured diamonds; A000447: "polar" structured meta-diamond; A006484 for other structured meta numbers; and A100145 for more on structured numbers.: James A. Record (james.record(AT)gmail.com). Nov 07, 2004

Cf. A059721, A059723.

Cf. A143803 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Sequence in context: A050479 A156674 A022277 this_sequence A074225 A055514 A055233

Adjacent sequences: A059719 A059720 A059721 this_sequence A059723 A059724 A059725

nonn

Henry Bottomley (se16(AT)btinternet.com), Feb 07 2001

Edited with new definition by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008