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A108195 n^2 + 5*n - 1. 5
5, 13, 23, 35, 49, 65, 83, 103, 125, 149, 175, 203, 233, 265, 299, 335, 373, 413, 455, 499, 545, 593, 643, 695, 749, 805, 863, 923, 985, 1049, 1115, 1183, 1253, 1325, 1399, 1475, 1553, 1633, 1715, 1799, 1885, 1973, 2063, 2155, 2249, 2345, 2443, 2543, 2645 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n>1: a(n) = A176271(n+2,n-1). - Reinhard Zumkeller, Apr 13 2010

a(n-2) = n*(n + 1) - 7, n>=0, with a(-2) = -7, a(-1) = -5 and a(0) = -1, gives the values for a*c of indefinite binary quadratic forms [a, b, c] of discriminant D = 29 for b = 2*n + 1. In general D = b^2 - 4*a*c > 0 and the form [a, b, c] is a*x^2 + b*x*y + c*y^2. - Wolfdieter Lang, Aug 16 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Greek Cross

Eric Weisstein's World of Mathematics, Gaullist Cross

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

FORMULA

a(n) = 2*n+a(n-1)+4, with n>1, a(1)=5. - Vincenzo Librandi, Nov 13 2010

G.f.: x*(5 + 3*x - x^2 - 5*x)/(1 - x)^3. - Vincenzo Librandi, Jun 11 2014

EXAMPLE

....... +---+ ......... The Cross of Lorraine

....... | + | ......... having n=2 crossbeams

... +---+---+---+ ..... consists of a(2)=13 squares

... | + | + | + |

... +---+---+---+

....... | + |

+---+---+---+---+---+

| + | + | + | + | + |

+---+---+---+---+---+

....... | + |

....... +---+

....... | + |

....... +---+

....... | + |

....... +---+

MAPLE

with (combinat):seq(fibonacci(3, n)+n-8, n=3..51); - Zerinvary Lajos, Jun 07 2008

MATHEMATICA

a=-14; lst={}; Do[a+=n; If[a>4, AppendTo[lst, a/2]], {n, 0, 6!, 4}]; lst...and/or... lst={}; Do[AppendTo[lst, n^2+5*n-1], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 01 2009 *)

CoefficientList[Series[(5 + 3 x - x^2 - 5 x)/(1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 11 2014 *)

PROG

(MAGMA) [n^2+5*n-1: n in [1..40]]; // Vincenzo Librandi, Jun 11 2014

(PARI) a(n)=n^2+5*n-1 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A002522.

Sequence in context: A129806 A125830 A049882 * A074798 A031336 A099958

Adjacent sequences:  A108192 A108193 A108194 * A108196 A108197 A108198

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Jun 15 2005

STATUS

approved

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Last modified June 22 23:15 EDT 2017. Contains 288633 sequences.