A261418 The UUDDUUD sequence, or the 3/7 sequence: start with 4, then successively add or subtract the integers 1,2,3,..., using the repeating sign pattern + + - - + + -.

4, 5, 7, 4, 0, 5, 11, 4, 12, 21, 11, 0, 12, 25, 11, 26, 42, 25, 7, 26, 46, 25, 47, 70, 46, 21, 47, 74, 46, 75, 105, 74, 42, 75, 109, 74, 110, 147, 109, 70, 110, 151, 109, 152, 196, 151, 105, 152, 200, 151, 201, 252, 200, 147, 201, 256, 200, 257, 315, 256, 196, 257, 319, 256, 320, 385, 319, 252, 320, 389, 319, 390, 462, 389, 315, 390, 466, 389, 467, 546, 466, 385, 467, 550, 466, 551, 637, 550, 462, 551, 641, 550

Offset

0,1

Comments

Each numbers appears two or three times. Only 3/7 of the integers appear, namely 7 times the triangular numbers plus (0,4,5) or (5,4,0).

References

Ed Pegg, Jr., Posting to Math Fun Mailing List, Aug 26 2015

Links

Table of n, a(n) for n=0..91.

Wolfram Demonstrations Project, Semigraceful Eulerian Graphs

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,2,-2,0,0,0,0,0,-1,1).

Formula

G.f.: ( -4-x -2*x^2 +3*x^3 -5*x^5 -6*x^6 +15*x^7 -6*x^8 -5*x^9 +4*x^10 -2*x^12 -x^13 +4*x^4 +3*x^11 -4*x^14 ) / ( (x^6+x^5+x^4+x^3+x^2+x+1)^2 *(x-1)^3 ). - R. J. Mathar, Jul 27 2016

Example

The first differences are
1, 2, -3, -4, 5, 6, -7,
8, 9, -10, -11, 12, 13, -14,
15, 16, -17, -18, 19, 20, -21,
22, 23, -24, -25, 26, 27, -28,
...

Mathematica

FoldList[Plus, 4, Flatten[Table[{1, 1, -1, -1, 1, 1, -1}, {20}]] Range[140]]

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, -1, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1]^n*[4; 5; 7; 4; 0; 5; 11; 4; 12; 21; 11; 0; 12; 25; 11])[1, 1] \\ Charles R Greathouse IV, Sep 01 2015

Crossrefs

Sequence in context: A272005 A274984 A114343 * A011457 A016720 A104140

Adjacent sequences: A261415 A261416 A261417 * A261419 A261420 A261421

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 27 2015

Status

approved