

A134483


Triangle read by rows: T(n,k)=2n+k2; 1<=k<=n.


2



1, 3, 4, 5, 6, 7, 7, 8, 9, 10, 9, 10, 11, 12, 13, 11, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 21, 22, 17, 18, 19, 20, 21, 22, 23, 24, 25, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
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OFFSET

1,2


COMMENTS

Row sums = the heptagonal numbers, A000566: (1, 7, 18, 34, 55, 81,...).
Row n consists of n consecutive integers starting with 2n1.  Emeric Deutsch, Nov 04 2007


LINKS

Boris Putievskiy, Rows n = 1..140 of triangle, flattened
Boris Putievskiy, Transformations [of] Integer Sequences And Pairing Functions, 2012, arXiv:1212.2732 [math.CO].


FORMULA

T(n,k)=2n+k2 for 1<=k<=n. G.f.= tz(1+z+2tz4tz^2)/[(1z)^2(1tz)^2]  Emeric Deutsch, Nov 04 2007
From Boris Putievskiy, Jan 16 2013: (Start)
a(n) = A002260(n)+2*A003056(n)
a(n) = i+2*t, where i=nt*(t+1)/2, t=floor((1+sqrt(8*n7))/2). (End)


EXAMPLE

First few rows of the triangle are:
1;
3, 4;
5, 6, 7;
7, 8, 9, 10;
9, 10, 11, 12, 13;
...


MAPLE

for n to 10 do seq(2*n+k2, k=1..n) end do; # yields sequence in triangular form  Emeric Deutsch, Nov 04 2007


CROSSREFS

Cf. A000566.
Sequence in context: A196119 A225852 A198458 * A121151 A088243 A154660
Adjacent sequences: A134480 A134481 A134482 * A134484 A134485 A134486


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Oct 27 2007


STATUS

approved



