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A134483 Triangle read by rows: T(n,k)=2n+k-2; 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 (list; table; graph; refs; listen; history; text; internal format)
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 2n-1. - 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+k-2 for 1<=k<=n. G.f.= tz(1+z+2tz-4tz^2)/[(1-z)^2(1-tz)^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=n-t*(t+1)/2, t=floor((-1+sqrt(8*n-7))/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+k-2, 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

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Last modified October 19 04:10 EDT 2019. Contains 328211 sequences. (Running on oeis4.)