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A164897 a(n) = 4*n*(n+1) + 3. 6
3, 11, 27, 51, 83, 123, 171, 227, 291, 363, 443, 531, 627, 731, 843, 963, 1091, 1227, 1371, 1523, 1683, 1851, 2027, 2211, 2403, 2603, 2811, 3027, 3251, 3483, 3723, 3971, 4227, 4491, 4763, 5043, 5331, 5627, 5931, 6243, 6563, 6891, 7227, 7571, 7923, 8283, 8651, 9027, 9411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

One-fourth the sum of the three terms produced by the division of complex numbers (2*n-3+(2*n-1)*i)/(2*n+1+(2*n+3)*i). For (b+c*i)/(d+e*i) the three terms in parentheses are ((b*d+c*e)+(c*d-b*e)*i/(d^2+e^2). By substituting b=2*n-3, c=2*n-1, d=2*n+1, and e=2*n+3 one gets a(n). - J. M. Bergot, Sep 10 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..900

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

FORMULA

a(n) = A000124(2*n) + A000124(2*n+1) = A069894(n)+1.

a(n+1) - a(n) = 8n+8 = A008590(n+1) (first differences).

a(n+1) - 2*a(n) + a(n-1) = 8 = A010731(n) (second differences).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>2.

G.f.: (3+2*x+3*x^2) / (1-x)^3.

Sum_{k=n+1..2*n+1} a(k) - Sum_{k=0..n} a(k) = (2*n+2)^3. - Bruno Berselli, Jan 24 2011

E.g.f.: (4x^2 + 8x + 1)*exp(x). - G. C. Greubel, Sep 22 2015

MAPLE

A164897:=n->4*n*(n+1)+3: seq(A164897(n), n=0..100); # Wesley Ivan Hurt, Sep 10 2015

MATHEMATICA

Table[4 n (n + 1) + 3, {n, 0, 50}] (* Harvey P. Dale, Jan 23 2011 *)

PROG

(MAGMA) [4*n*(n+1)+3: n in [0..50]]; // Vincenzo Librandi, Apr 24 2011

(PARI) a(n)=4*n*(n+1)+3 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000124, A008590, A010731, A016743, A069894.

Sequence in context: A123928 A186301 A170945 * A212982 A164845 A024194

Adjacent sequences:  A164894 A164895 A164896 * A164898 A164899 A164900

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 30 2009

EXTENSIONS

Definition simplified by R. J. Mathar, Sep 16 2009

STATUS

approved

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Last modified October 23 22:26 EDT 2017. Contains 293833 sequences.